A future for Ukrainian science.

As the war in Ukraine enters its fourth month, Russian forces continue to destroy the nation's scientific institutions and infrastructure, signaling Russia's intent to obliterate the future for Ukraine. In Kharkiv, for instance, the renowned Institute of Physics and Technology and its newly built Neutron Source nuclear facility have been heavily damaged. Even the Plant Production Institute with its underground national seed bank-one of the world's largest-has been bombed.

Stochastic processes crossing from ballistic to fractional diffusion with memory: exact results.

We address the now classical problem of a diffusion process that crosses over from a ballistic behavior at short times to a fractional diffusion (subdiffusion or superdiffusion) at longer times. Using the standard non-Markovian diffusion equation we demonstrate how to choose the memory kernel to exactly respect the two different asymptotics of the diffusion process. Having done so we solve for the probability distribution function (pdf) as a continuous function which evolves inside a ballistically expanding domain.